# Best choice of estimators in a CFA analysis without full dataset?

My team and I are working on an assignment that provided:

• A model to be tested, consisting of 2 Factors explaining 6 variables; $$F1$$ would be explained by $$X1, X2$$ and $$X3$$, while $$F2$$ would be explained by $$X4, X5$$ and $$6$$;
• Besides that, we are informed about the sample ($$N=100$$) observations for each $$X$$;
• The Standard Deviations for each variable;
• We are supposed to test the model fit using CFA;

With that info, we were able to get the covariance matrix and run a CFA through SAS/R without major issues. The thing is: apparently it is important to assume normality to be able to use the ML estimator. What are our alternatives if we didn't want to simply "assume normality"? Are there ways to use different estimators without knowing the means, or the full data set? Thank you immensely for any insights provided.

• If you dont' have the raw data, you're pretty much stuck with ML (or something like GLS or ULS, which are rarely recommended for anything). – Jeremy Miles Oct 29 '19 at 16:02
• @Pedro Alonso, note that if you're testing a correlated two-factor model, it will NOT be identified with two factors and 3 items each unless you introduce constraints. As for the missing techniques, ML is one option. Another option would be to use Multiple Imputation. But what is the proportion of missing data? And also what's the missing data mechanism? ML fares well under "Missing at Random (MAR) or Missing Completely at Random "MCAR" but not under non-missing at random "NMAR" – PsychometStats Oct 29 '19 at 18:30
• That's the thing - my issue is not the classic missing data, we were simply not given raw data, at all. We had to work only with a corr matrix, sd's and sample size. That was all we knew about the original variables. – Pedro Alonso Nov 1 '19 at 15:35